Additively manufactured Nitinol (NiTi) architectured materials hold promising potential for applications like shock absorption, bone replacement implants, and solid-state refrigeration, owing to their customizable superelasticity and shape memory effect achieved through the structure and relative density of the unit cell. Despite these advantages, challenges persist in achieving large recoverable deformations in NiTi TPMS structures due to early fracture and uncontrollable properties initiated from the laser powder bed fusion (PBF) process. This research focuses on understanding the tension-compression asymmetry behavior in as-fabricated NiTi and its consequential impact on the local and global responses of NiTi TPMS structures. The study involves measurements of tension-compression asymmetry behavior under uniaxial conditions, along with characterization and analysis of the microstructure and elemental composition of as-fabricated NiTi. The identified asymmetry behavior is then integrated into finite element models to show its effect on the distribution of martensitic transformation and macroscopic functional response in TPMS structures. Building upon these analyses, aging heat treatment is used as a strategy to enhance the recoverable deformation of NiTi TPMS structures. This research aims to provide valuable insights into the modelling and fabrication of superelastic NiTi structures tailored for customized shape and recoverable deformation.